(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Glitzky, Annegret; Griepentrog, Jens André
We prove a discrete Sobolev-Poincare inequality for functions with
arbitrary boundary values on Voronoi finite volume meshes. We use Sobolev's
integral representation and estimate weakly singular integrals in the context
of finite volumes. We establish the result for star shaped polyhedral domains
and generalize it to the finite union of overlapping star shaped domains. In
the appendix we prove a discrete Poincare inequality for space dimensions
greater or equal to two.
